Estimate the indicated probability by using the normal distribution as an approximation to the binomial distribution.
-A certain question on a test is answered correctly by 22% of the respondents. Estimate the probability that among the next 150 responses there will be at most 40 correct answers.
A) 0.8997
B) 0.9306
C) 0.1003
D) 0.0694

Question

Quizplus · Accepted Answer

The normal distribution can be used to approximate the binomial distribution when n is large and p is not too close to 0 or 1. Here, n = 150 and p = 0.22. The mean (np) is 33 and the standard deviation (sqrt(np(1-p))) is approximately 5.33. Using the continuity correction, we find the z-score for 40.5 and calculate the cumulative probability, which is approximately 0.9306.

Estimate the Indicated Probability by Using the Normal Distribution as an Approximation